## Abstract Convexity, Weak Epsilon-Nets, and Radon Number

Let F be a family of subsets over a domain X that is closed under taking intersections. Such structures are abundant in various fields of mathematics such as topology, algebra, analysis, and more. In this talk we will view these objects through the lens of *convexity*.

We will focus on an abstraction of the notion of *weak epsilon nets*:

given a distribution on the domain X and epsilon>0,

a weak epsilon net for F is a set of points that intersects any set in F with measure at least epsilon.